The main point of the Gaussian, as I’ve said, is that most observations hover around the mediocre, the average; the odds of a deviation decline faster and faster (exponentially) as you move away from the average. If you must have only one single piece of information, this is the one: the dramatic increase in the speed of decline in the odds as you move away from the center, or the average. Look at the list below for an illustration of this. I am taking an example of a Gaussian quantity, such as height, and simplifying it a bit to make it more illustrative. Assume that the average height (men and women) is 1.67 meters, or 5 feet 7 inches. Consider what I call a
10 centimeters taller than the average (i.e., taller than 1.77 m, or 5 feet 10): 1 in 6.3
20 centimeters taller than the average (i.e., taller than 1.87 m, or 6 feet 2): 1 in 44
30 centimeters taller than the average (i.e., taller than 1.97 m, or 6 feet 6): 1 in 740
40 centimeters taller than the average (i.e., taller than 2.07 m, or 6 feet 9): 1 in 32,000
50 centimeters taller than the average (i.e., taller than 2.17 m, or 7 feet 1): 1 in 3,500,000
60 centimeters taller than the average (i.e., taller than 2.27 m, or 7 feet 5): 1 in 1,000,000,000
70 centimeters taller than the average (i.e., taller than 2.37 m, or 7 feet 9): 1 in 780,000,000,000
80 centimeters taller than the average (i.e., taller than 2.47 m, or 8 feet 1): 1 in 1,600,000,000,000,000
90 centimeters taller than the average (i.e., taller than 2.57 m, or 8 feet 5): 1 in 8,900,000,000,000,000,000
100 centimeters taller than the average (i.e., taller than 2.67 m, or 8 feet 9): 1 in 130,000,000,000,000,000,000,000
… and,
110 centimeters taller than the average (i.e., taller than 2.77 m, or 9 feet 1): 1 in 36,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000.
Note that soon after, I believe, 22 deviations, or 220 centimeters taller than the average, the odds reach a googol, which is 1 with 100 zeroes behind it.
The point of this list is to illustrate the acceleration. Look at the difference in odds between 60 and 70 centimeters taller than average: for a mere increase of four inches, we go from one in 1 billion people to one in 780 billion! As for the jump between 70 and 80 centimeters: an additional 4 inches above the average, we go from one in 780 billion to one in 1.6 million billion![51]
This precipitous decline in the odds of encountering something is what allows you to ignore outliers. Only one curve can deliver this decline, and it is the bell curve (and its nonscalable siblings).
By comparison, look at the odds of being rich in Europe. Assume that wealth there is scalable, i.e., Mandelbrotian. (This is not an accurate description of wealth in Europe; it is simplified to emphasize the logic of scalable distribution.)[52]
People with a net worth higher than €1 million: 1 in 62.5
Higher than €2 million: 1 in 250
Higher than €4 million: 1 in 1,000
Higher than €8 million: 1 in 4,000
Higher than €16 million: 1 in 16,000
Higher than €32 million: 1 in 64,000
Higher than €320 million: 1 in 6,400,000
Recall the comparison between the scalable and the nonscalable in Chapter 3. Scalability means that there is no headwind to slow you down.
Of course, Mandelbrotian Extremistan can take many shapes. Consider wealth in an extremely concentrated version of Extremistan; there, if you double the wealth, you halve the incidence. The result is quantitatively different from the above example, but it obeys the same logic.
People with a net worth higher than €1 million: 1 in 63
Higher than €2 million: 1 in 125
Higher than €4 million: 1 in 250
Higher than €8 million: 1 in 500
Higher than €16 million: 1 in 1,000
Higher than €32 million: 1 in 2,000
Higher than €320 million: 1 in 20,000
Higher than €640 million: 1 in 40,000
If wealth were Gaussian, we would observe the following divergence away from €1 million.
People with a net worth higher than €1 million: 1 in 63
Higher than €2 million: 1 in 127,000
Higher than €3 million: 1 in 14,000,000,000
Higher than €4 million: 1 in 886,000,000,000,000,000
Higher than €8 million: 1 in 16,000,000,000,000,000,000,000,000,000,000,000
Higher than €16 million: 1 in …
What I want to show with these lists is the qualitative difference in the paradigms. As I have said, the second paradigm is scalable; it has no headwind. Note that another term for the scalable is power laws.
Just knowing that we are in a power-law environment does not tell us much. Why? Because we have to measure the coefficients in real life, which is much harder than with a Gaussian framework. Only the Gaussian yields its properties rather rapidly. The method I propose is a general way of viewing the world rather than a precise solution.
Remember this: the Gaussian-bell curve variations face a headwind that makes probabilities drop at a faster and faster rate as you move away from the mean, while “scalables”, or Mandelbrotian variations, do not have such a restriction. That’s pretty much most of what you need to know.[53]
Let us look more closely at the nature of inequality. In the Gaussian framework, inequality decreases as the deviations get larger – caused by the increase in the rate of decrease. Not so with the scalable: inequality stays the same throughout. The inequality among the superrich is the same as the inequality among the simply rich – it does not slow down.[54]
Consider this effect. Take a random sample of any two people from the U.S. population who jointly earn $1 million per annum. What is the most likely breakdown of their respective incomes? In Mediocristan, the most likely combination is half a million each. In Extremistan, it would be $50,000 and $950,000.
